Biology Reference
In-Depth Information
As we shall see, oscillations in endocrine physiology are often caused by
(delayed) feedback loops. We begin with a heuristic explanation of this
behavior.
Recall from Chapter 2 that if a system has a stable equilibrium state, its
values stabilize around this state in the long run (i.e., the limit for t
!1
of the variable as a function of time is equal to the equilibrium state).
An oscillatory system must include a restorative process that keeps
the system close to its steady state, and oscillations can be sustained
only if other factors, like inertia in physical systems, lead to
overshooting the equilibrium value. For most cellular, endocrine, and
neuronal oscillations, the critical factor that provides an overshoot
is delay, which prevents the feedback restorative process from coming
into full play until the equilibrium value has been passed (see
Example 10-1).
Delays in biological systems can arise from many sources, and the
debate about what causes delay and how best to model complex systems
involving delay is far from over. The simplest situations involving
delay are those with a certain time-offset or lag between an action
triggered by one variable and the response to this action by a second
variable. For example, suppose hormones A and B are involved in the
control of a particular organismal function, and that hormone B turns off
the production of hormone A. Suppose also that the inhibitory effect of
Hormone B does not immediately follow an increase of hormone B
in the bloodstream. The time elapsed between the increase in the
concentration of B and the decrease in the concentration of A will be
interpreted in the simulations below as an explicit delay. An explicit delay
generally represents the amount of time necessary for a certain sequence
of molecular and/or cellular events to occur. Explicit delays can vary
greatly, depending upon the system at hand—the incubation period
for an infectious disease represents one kind of explicit delay, and
incubation periods can range from days to years. In this case, the delay
results from the amount of time it takes for the pathogen to travel
through the host's body and to multiply in the favored portion of the
host's anatomy.
In other cases, the delay may not be explicit. In such cases, the delay
would not formally reflect a certain period of time, but would result
from a particular threshold value that must be met before the affected
variable responds. In our hormone example (above), let us say that the
level of hormone A will not be affected until the level of hormone B
in the bloodstream reaches 300 pg/ml (picograms per milliliter). The
delay then reflects the time necessary for the concentration of B to rise
from its baseline levels and approach the threshold of 300 pg/ml. For
another example, consider the Lotka-Volterra predator-prey model
described by a coupled system with threshold values for the predator
and prey populations (see Example 10-2). The population of the predator
